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Published equation contexts

⟨e−βW⟩=e−βΔF\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}

Why this formula appears here

Because these three frameworks share vocabulary, it is worth being explicit about the one place where a formal expression clarifies rather than decorates the comparison: the Jarzynski equality itself. Written compactly, it states ⟨e−βW⟩=e−βΔF\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}. where W is the work performed on the system along a single nonequilibrium trajectory, Δ\Delta F is the equilibrium free-energy difference between the initial and final states, and β\beta is inverse temperature. The average on the left is taken over repeated realizations of the same driving protocol, each of which can dissipate a different amount of work due to thermal fluctuations. The identity holds exactly regardless of how fast or far from…

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e−βWe^{-\beta W}

Symbol e^-β W

e−e^-β W is part of the quantity the equation computes from the expression on the right.

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e−βΔFe^{-\beta \Delta F}

Symbol e^-β Δ F

e−e^-β Δ F is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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⟨e−βW⟩=e−βΔF\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}

Equation 1 · Physics

Three Ways to Measure a System That Refuses to Settle Down

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Because these three frameworks share vocabulary, it is worth being explicit about the one place where a formal expression clarifies rather than decorates the comparison: the Jarzynski equality itself. Written compactly, it states ⟨e−βW⟩=e−βΔF\left\langle e^{-\beta W} \right\rangle = e^{-\beta \Delta F}. where W is the work performed on the system along a single nonequilibrium trajectory, Δ\Delta F is the equilibrium free-energy difference between the initial and final states, and β\beta is inverse temperature. The average on the left is taken over repeated realizations of the same driving protocol, each of which can dissipate a different amount of work due to thermal fluctuations. The identity holds exactly regardless of how fast or far from…

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